Integrals and Series Representations of q-Polynomials and Functions: Part II Schur Polynomials and the Rogers-Ramanujan Identities

2016/05/09 by Mourad E. H. Ismail, Ismail, Mourad E. H., Ruiming Zhang +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1605.02728

openalex publication_date 2016/05/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We give several expansion and identities involving the Ramanujan function A_q and the Stieltjes--Wigert polynomials. Special values of our idenitities give m-versions of some of the items on the Slater list of Rogers-Ramanujan type identities. We also study some bilateral extensions of certain transformations in the theory of basic hypergeometric functions.

Citations

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

Related

• q-Bessel Functions and Rogers-Ramanujan Type Identities
• Integral and Series Representations of q-Polynomials and Functions: Part I
• Simple proofs of Bressoud's and Schur's polynomial versions of the Rogers-Ramanujan identities
• Rogers-Ramanujan type identities and Chebyshev Polynomials of the third kind
• Some q-transformation formulas and Rogers-Ramanujan type identities